``Sobel edge operator'' - Sobel edge operator

VFX name:

iSobel

IMPROMPTU Equivalent:

Sobel_Operator

purpose:

Calculate the edge strengths (or direction) of voxels in a 3-D grayscale volume using the Sobel edge operator. The edge strengths are calculated using either a 2-D Sobel operator or a 3-D Sobel operator depending on the option chosen.

input:

An 8-bit 3-D grayscale volume.

output:

An 8-bit volume.

parameters:

Default parameters menu is

Function = 2D-MAGNITUDE
sobel_direction = TRANSVERSE
Gradient_type = Gradient_magnitude
sobel_threshold = 4
input from vol # = 0
copy output to vol # = 0

The Sobel operator is made up of a number of options. Depending on the option chosen (as specified by the parameter "function") the Sobel algorithm can calculate the 2D Gradient Magnitude/2d Gradient direction/ 3D Gradient magnitude using the 2D Sobel operator/3D Sobel operator. The use of the 2-D Sobel operator can be done in either of the Transverse/Coronal/Sagittal directions (as specified by the "sobel_direction" option). When computation of the gradient magnitude is desired, there exist 2 choices. The gradient can either be chosen as the maximum of the gradients in the individual directions or as the sum of the square root of the gradients in the individual directions. (as specified by the "gradient_type" option). The ouput image of the gradient magnitude option is a thresholded image. The value of the threshold is to be supplied by the user using the "sobel_threshold" option. In the output image, all gray-scale values below the threshold are reset to zero. Gray-scale values above the threshold are not altered. The output image of the "2-D direction" option is a gray-scale image indicating the direction of the gradient in degrees. The entire range of the angles between [-90,+90] has been scaled by a factor of two and "shifted" by +128 degrees so that zero angle corresponds to a gray-scale value of 128. The angle of the gradient is measured from the x-axis (for transverse and coronal directions) and from the y-axis for the sagittal direction.

comments:

See below.

1.

The 2-d Sobel operator is a moderately time-consuming operation (if the number of slices used is large). The 3-D Sobel operator is more time consuming than its 2-D counterpart and could be fairly time-consuming if a large volume of the image is used in computing the edge gradient.